Kira Q Tech, developer of KQ MiniSynth released KQ Dixie! This is a 6-operator FM synth based so closely on the Yamaha DX7 that it is almost entirely compatible with DX7 SysEx! When connected to a real DX7 you could use this to manage your preset library.

KQ Dixie arrives with AUv3 and Audiobus. The app is Universal and will run on devices down to iOS 9.Update: But as Bob noted in the comments here, it is limited to 64-bit devices.

KQ Dixie iTunes Description:

KQ Dixie is a 6-Operator FM synthesizer that is modeled on the synthesizer which appeared on the 1980s.

FM synthesizers make sounds with Frequency Modulation.
FM brings rich and brilliant sounds which are impossible to create with analog one.
It makes very complex waves with simple modulations.
The same method is used for a radio.
The synthesizer gained much popularity in the 1980s.

This app lets you make sounds freely with 156 voice parameters.
Almost all parameters are compatible with DX7.

Audio Unit v3 compatible.
Audiobus compatible.
32 algorithms included.
You can manage the hardware DX7 when it is connected with external MIDI cables.
Supports DX7 System Exclusive Messages (SysEx) and syx files.
Supports Zip files.
You may be able to find a lot of patches on the internet.

Yamaha DX7 is a trademark of Yamaha Corporation.
I have no business relations with Yamaha.